The boy likes numbers. He has a sheet of paper.
He have written a sequence of consecutive integer numbers
on the sheet. The boy likes them.

But then the girl came. The girl is cruel. She
changed some of the numbers.

The boy is disappointed. He cries. He does not like
all these random numbers. He likes consecutive numbers.
He really likes them. But his numbers are not
consecutive any more. The boy is disappointed. He cries.

Help the boy. He can change some numbers. He would
not like to change many of them. He would like to change
as few as possible. He cannot change their order.
He would like the numbers to be consecutive again.
Help the boy.

Input

The first line of the input file contains n --- the number
of numbers in the sequence (1 ≤ n ≤ 50000). The next
line contains the sequence itself --- integer numbers
not exceeding 109 by their absolute values.

There are multiple cases. Process to the end of file.

Output

Output the minimal number of numbers that the boy must change.
After that output the sequence after the change.